Dear Henry,
See if the following is of some help:
Please see page 15-7 of the LS-DYNA User’s Manual:
"LS-DYNA Keyword User's Manual - Volume I", LS-DYNA Dev/Revision 13586,
Livermore Software Technology Corporation, Livermore, California, March, 2021.
http://ftp.lstc.com/anonymous/outgoing/jday/manuals/DRAFT_Vol_I.pdf
4. Formulation. With mass proportional system damping the acceleration is
computed as:
𝐚𝑛 = 𝐌−1(𝐏𝑛 − 𝐅𝑛 − 𝐅dampn)
where, 𝐌 is the diagonal mass matrix, 𝐏𝐧 is the external load vector, 𝐅𝑛 is the
internal load vector, and 𝐅damp𝑛 is the force vector due to system damping. This
latter vector is defined as:
𝐅damp𝑛 = 𝐷𝑠𝑚𝐯
The best damping constant for the system is usually some value approaching
the critical damping factor for the lowest frequency mode of interest.
(𝐷𝑠)critical = 2𝜔min
The natural frequency 𝜔min (given in radians per unit time) is generally taken as
the fundamental frequency of the structure. This frequency can be determined
from an eigenvalue analysis or from an undamped transient analysis. Note that
this damping applies to both translational and rotational degrees of freedom.
Also note that mass proportional damping will damp rigid body motion as well
as vibration.
Energy dissipated by through mass weighted damping is reported as system
damping energy in the ASCII file glstat. This energy is computed whenever
system damping is active.
------------------------------
Some additional notes:
https://www.dynasupport.com/howtos/general/damping
Mass damping in LS-DYNA, which includes *DAMPING_GLOBAL and *DAMPING_PART_MASS, is intended to damp low-frequency structural modes but it has the added effect of damping rigid body modes. Thus parts that undergo significant rigid body motion should be excluded from mass damping (or the mass damping should be turned off during the time the part undergoes rigid body motion). The critical mass damping coefficient is 4*pi/T where T is the period of the mode targeted for damping (usually the lowest frequency (fundamental) mode). The period can be determined from an eigenvalue analysis or estimated from results of an undamped transient analysis. In version 970, *DAMPING_RELATIVE provides a means to invoke mass damping which is relative to the motion of a particular rigid body.
Damping is completely optional. If the user decides to use mass damping, a damping coefficient less than the critical damping coefficient is suggested. A value of 10% of critical damping, or 0.4*pi/T is fairly typical. You can choose to damp all parts using the same damping coefficient (*DAMPING_GLOBAL) or, to tailor the damping to the individual response characteristics of each part, you can assign a different damping coefficient to each part (*DAMPING_PART_MASS). In either case, the damping coefficient can vary with time (useful to turn damping off or on in the middle of a simulation).
------------------------------
https://www.dynaexamples.com/introduction/examples-manual/misc/damping
Sincerely,
James M. Kennedy
KBS2 Inc.
August 17, 2021
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